Question

Will give a medal and fan...


Mike was working on solving the exponential equation 37x = 12; however, he is not quite sure where to start. Using complete sentences, describe to Mike how to solve this equation and how solving would be different if the bases were equal.

Answer 1

If
\[a^x = b\]
then
\[x = \log_{a} b\]
If bases are equal
\[a^x = a^n\]
then you can just set exponents equal
\[x = n\]

Answer 2

So,

37x=12

Then, x=log37 (12)

What do you mean if the bases are equal?

Answer 3

\[37^x = 37^4\]
you dont have to use log
just say x = 4

Answer 4

Ohhhh okay! That makes so much more sense. Thank you!!! :D

Answer 5

yw :)